3.9 Exponential and Logarithmic Derivatives Thurs Nov 19

1
3.9 Exponential and Logarithmic DerivativesThurs
Nov 19

• Do Now
• Find the derivatives of
• 1)
• 2)

2
HW Review p.219 9-20

• 9)
• 10)
• 11)
• 12)
• 13)
• 14)
• 15)
• 16)
• 17)
• 18)
• 19)
• 20)

3
HW Review p.219 21-26

• 21)
• 22)
• 23)
• 24)
• 25)
• 26)
• 27) 3sec2 4x (sec4xtan4x) (4)
• 28) esin2x (cos2x) (2)
• 32) on board
• 33) (1/2) (sinx2)-1/2 (cosx2)(2x)

4
Exponential Logarithmic Functions

• Logarithmic and exponential functions are among
  the most common functions encountered in
  applications.
• Population curves consist of logarithmic
  functions, particularly the natural logarithm.
• Growth/Decay, business applications use
  exponential functions

5

• Thm- For any constant b gt 0,
• Thm- In particular,

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Derivative of Natural Log

• To determine the derivative of the natural
  logarithm, lets take a look at the graph of lnx
  and its slopes

7
Derivative of ln x contd

• Thm- For x gt 0,

8
Example

• Find the derivative of f(x) x ln x and g(x) x
  10x

9
Closure

• Hand in Find the derivative of the following
  functions
• 1)
• 2)
• HW p.187 1-19 odds, 25-31 odds

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Logarithmic DifferentiationFri Nov 20

• Do Now
• Find the derivative
• 1)
• 2)

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HW Review p.187 1-19 25-31

• 1) lnx 1 19)
• 3) (2/x) lnx 25) y 36ln6(x-2) 36
• 5) 27) y 320 ln3(t-2) 318
• 7) 29) y 5-1
• 9) 31) y -1(t-1) ln4
• 11)
• 13)
• 15)
• 17)

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Logarithmic Differentiation

• Logarithmic Differentiation can be used in place
  of several product/quotient rules
• Ex

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Logarithmic Differentiation

• 1) Take ln of both sides
• 2) Use log rules to separate each factor
• 3) Differentiation both sides (chain rule)
• 4) Multiply by f(x) (original)

14
Ex

• Use log differentiation

15
Ex 2

• Differentiate using log dif.

16
Closure

• Find the derivative using logarithmic
  differentiation
• HW p.187 37-43 odds

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Other base Log DerivativesMon Nov 23

• Do Now
• Find the derivative
• 1)
• 2)

18
HW Review p.187 37-43

• 37) 2x 14
• 39) 3x2 - 12x 79
• 41)
• 43)

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Other Base Logarithms

• We can calculate the derivative of other base
  logs by using the change-of-base formula using ln
  x

20
Ex

• Find the derivative of

21
You try

• Find the derivatives
• 1)
• 2)

22
Closure

• Journal Entry Write about the derivatives of
  logarithms. How can we calculate them? How can
  they be useful when we have complicated
  functions?
• HW p.187 21-24